Binary Search Logic
Updated 2026-08-10
INTRODUCTION
English translation pending.
CORE DEFINITION
In an ordered sequence, compare the midpoint against the target and discard half of the range each time, which locates the target in logarithmic time. As a scaffold it is exponential speedup: a thousand options can be settled with only ten comparisons, provided that the sequence has been sorted beforehand.
SCAFFOLDING EFFECT
Reduce cognitive load
- Sort first: confirm the set really is ordered, or the whole method fails. - Middle probe: compare the midpoint against the criterion you are hunting for. - Half cut: go left when it is less, and go right when it is more.
Anchor fast decisions
In an ordered set you compare at the midpoint and halve the candidate range each step, so n items take at most log base two of n comparisons, an O of log n cost. The crux is the sorted precondition, which is what makes discarding half a safe move rather than a gamble.
MINIMUM ACTION
In progress 0/2Practice this model in one real situation:
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Source support: Explicit
- en.wikipedia.orghttps://en.wikipedia.org/wiki/Binary_searchverified
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